these two kinds of relaxation can be interpreted with "Stillinger model". In the framework of Stillinger’s model of inherent structures:
α-relaxation involves the sampling of deep, separated potential energy minima,
β-relaxation involves the sampling of adjacent and shallow minima
so to keep it simple and clear its better say :
α-relaxation refers to the cooperative relaxation of molecules that occurs on the order of 1–10 s or longer.
β-relaxation is faster and refers to noncollective motion that occurs in the range of 10-5 s and shorter.
A high level explanation for these two types of relaxation can be found in an informative book in chapter 13 page 328 by Professor ARUN K. VARSHNEYA and